function X = saturate(U,alf)
N = length(U);
X = {};
fprintf('U = {%s} \n',cell2str(U,','));
PROGstart(2^N-1,'saturating...');
%fprintf('saturating...');
for i=1:2^N-1
  setstr = dec2bin(i,N);
  ii1 = find(setstr=='1');
  A = U(ii1);
  %fprintf('%d of %d: A = {%s} \n',i,2^N-1,cell2str(A,','));
  MA = AB2M(A,alf);
  B = setdiff(U,subs(A));
  %fprintf('%d of %d: B = {%s} \n',i,2^N-1,,cell2str(B,','));
  MB = AB2M(B,alf);
  % x must contain all the features of A
  % and none of B
  Minter = intersects(MA,alf);
  Munion =     unions(MB,alf);
  MAlessB = diff_dfsa(Minter,Munion);
  [b,x] = accept_str(MAlessB);
  %fprintf('b = %d, x = [%s] \n',b,x);
  if b
    X{end+1} = x;
  end
  PROGupdate(i);
end
PROGend
return

function M = unions(MM,alf)
M = null_dfsa(alf);
for i=1:length(MM)
  M = union_dfsa(M,MM{i});
end
return

function MM = AB2M(AB,alf)
MM = {};
for i=1:length(AB)
  MM{i} = shuf2dfsa(AB{i},alf);
end
return

function M = intersects(MM,alf)
M = all_dfsa(alf);
for i=1:length(MM)
  M = intersect_dfsa(M,MM{i});
end
return


function S = subs(A)
S = {};
for i=1:length(A)
  Si = all_subseq(A{i});
  S = unique([S(:); Si(:)]);
end
return